What approach should I use to detect faces in video game footage?
At first, you can find lots of information as pedestrian detection. As you are trying to localize game characters, the face is not the best option. You need to look for the character in general. 

About HAAR Cascades, the algorithm is one of the fastest face localization solutions in the market. The reason is, it applies all the feature classifications layer by layer, by starting from the wider feature. So, if it fails, it does not spend the time to check computationally intensive features. It was good until DNN overcome its success rate. However, it is not the best approach for recognizing game characters/pedestrians.

Also, it seems like you are overfitting the cascade so it stops and does not learn anything valuable. You can search methods about how to reduce overfit problem.

In 2005, a new method has been proposed, HOG (Histogram Of Gradients). You can use this one and classify output features to get what you desire. If you would like to go for deep learning version, I would suggest you to investigate how DNN is working, which kind of input images you need, what are the localization networks (i.e. YOLO, Faster R-CNN), how they are working.